1
Supplementary Methods
Species included in analysis. The 51 species used in all British butterfly analyses were
as follows (see below for explanation of numbers in parentheses): Aglais urticae (5, 7),
Anthocharis cardamines (4, 8, 10), Apatura iris, Aphantopus hyperantus (2, 5, 6, 7, 9),
Argynnis adippe (9), Argynnis aglaja (4, 5, 6, 7, 8, 10), Argynnis paphia (3, 10), Aricia
agestis (1, 2, 8, 9), Aricia artaxerxes, Boloria euphrosyne (2, 5), Boloria selene (1, 10),
Callophrys rubi (3, 4, 6, 7), Carterocephalus palaemon (4), Celastrina argiolus (9),
Coenonympha pamphilus, Coenonympha tullia, Cupido minimus (6, 8), Erebia aethiops
(1, 3, 6, 7), Erebia epiphron (3, 9), Erynnis tages (1, 3), Euphydryas aurinia (1, 3, 6),
Gonepteryx rhamni (4), Hamearis lucina (2), Hesperia comma (2), Hipparchia semele,
Inachis io, Lasiommata megera (8, 10), Leptidea sinapis (10), Limenitis camilla (2, 5),
Lycaena phlaeas, Maniola jurtina (3, 8), Melanargia galathea (6, 8, 9), Neozephyrus
quercus (1, 5, 6), Ochlodes venata (2, 8), Pararge aegeria (1), Pieris brassicae (2, 5),
Pieris napi, Pieris rapae (2, 10), Plebejus argus (4, 8), Polygonia c-album (3, 7),
Polyommatus bellargus (1, 7, 9), Polyommatus coridon (1, 2, 5, 9), Polyommatus icarus
(9), Pyrgus malvae (7), Pyronia tithonus (6), Satyrium pruni (3, 4, 5), Satyrium walbum (4, 6, 9, 10), Thecla betulae (8, 10), Thymelicus acteon (3, 4, 7), Thymelicus
lineola (1, 5), Thymelicus sylvestris (4, 7, 10).
Phylogenetic regression. Phylogenetic generalised least squares (GLS) regressionsS1
were carried out using the software package COMPARES2, that incorporates a single
parameter (α) to estimate the level of evolutionary constraint acting on a variable. Small
values of α suggest a strong effect of phylogenetic relatedness, whilst large values
suggest that comparative data are independent of phylogeny. We ran phylogenetic GLS
regressions based on a published working phylogeny for British butterfliesS3, using
maximum likelihood estimation of α up to a possible maximum of 15.5. The
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significance of these regressions was tested using the Pearson correlation coefficient (R)
for N-2 degrees of freedomS4, S5.
The large maximum likelihood estimates for the parameter α (Supplementary
Table 1) suggest that the evolutionary constraint acting on distribution pattern, size and
change was small. Parameter estimates and the proportion of variation in distribution
change explained by distribution pattern and size, given the maximum likelihood
estimates of α, are consistent with those presented in the main text (Supplementary
Table 1).
Sensitivity to sample size. Regressions of change against Dij (10-100 km) and AOO (10
km) were carried out for each of ten randomly selected sets of ten species. The species
that comprised each numbered set are shown by the numbers in parentheses in the
species list (above). In all ten cases these regressions included a positive effect of Dij,
combined in nine out of ten cases with a negative effect of AOO, and in one case
(random set 6) a positive effect of AOO. These regression equations were used to
predict change in the remaining 41 species, for which observed change was regressed
against expected change (Supplementary Table 2). From these ten regressions, the
mean raw R2 of observed versus expected change was 0.37, ranging from a minimum of
0.30 (random set 6) to a maximum of 0.45 (R2 for phylogenetic GLS regressions ranged
from 0.29 to 0.45, also with a mean of 0.37). The slopes of the relationship ranged from
0.33 to 1.70, with an average of 0.87. Thus the small samples of species predicted
relative rates of decline among species (R2) rather more consistently than absolute rates
of decline (slope). The former is important for choosing priorities in biodiversity
assessment, although the latter may be important for species classification based on
threshold levels of decline.
Sensitivity to scale. Dij was calculated as described in the main text and also using a
range of different combinations of cell sizes: 1) 10-20 km; 2) 10-50 km; 3) 10-100 km
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(the scale used in the main text); 4) 20-50 km; 5) 20-100 km; 6) 50-100 km. Linear
regressions of change in distribution size were carried out against Dij for each scale
combined with AOO calculated using the area of occupied fine scale cells for each
resolution (i.e. 10 km cells for analyses 1, 2 and 3; 20 km cells for analyses 4 and 5; 50
km cells for analysis 6), assuming that this area represented the finest scale information
available.
Dij values calculated for each species at the six different scales were highly
positively correlated (Spearman’s rank correlations, rs > 0.78, P < 0.001 in all cases;
Supplementary Table 3). For all six analyses, change in distribution size was
significantly positively related to Dij, combined with in five cases a significant negative
effect of AOO, and in one case (the coarsest scale, 50-100 km) a non-significant
negative effect of AOO (Supplementary Table 4). The strength of the relationship
declined with increasing coarseness of scale, with a maximum R2 of 0.52 for the 10-20
km scale (phylogenetic GLS R2 = 0.51). The scale reported in the main text (10-100
km) produced results that were intermediate between the strongest (fine scale) and
weakest (coarse scale) results.
Alternative measures of aggregation. Two further methods were used to quantify the
aggregation of species distribution patterns. In the first method, the mean number of
distribution records in circular radii of 10, 20, 50 and 100 km around each 10 km
distribution record were calculated for each species using Spatial Analysis For
Ecologists (SAFE) softwareS6. The mean number of records in each radius was divided
by the maximum number of records possible given a circle of that size, respectively 4,
12, 80, and 316 for each radius, giving a value between 0 and 1 for each radius for each
species which we refer to as Dx (analogous to Dx in supplementary reference S7, and
related to the cluster dimension measure of aggregationS8, S9).
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As a further related measure of aggregation, Ripley’s K function was calculated
for each speciesS10, S11. Ripley’s K function computes the mean number of points lying
within a circular search window of radius t around each distribution record, and divides
this value by the total number of distribution records. For a radius of t, the expected
number of distribution records under complete spatial randomness (with a Poission
point pattern process) is πt2; to linearize and stabilize variances, Ripley’s L (t) can be
calculated from Ripley’s K (t) as L (t) = ( K (t) / π )1/2. Ripley’s L has an expected value
of 0 under complete spatial randomness, with positive values indicating aggregation and
negative values segregation. Ripley’s L was calculated for radii of 10, 20, 50 and 100
km, using a spatial point-pattern analysis (splancs) program for the statistical
environment R (supplementary reference S12). For this analysis, Ripley’s L was
computed for each species assuming a rectangular study area with southwest and
northeast corners at the respective southwest and northeast corners of the British coast.
Edge effects on each of the alternative measures of aggregation were minimised by only
calculating up to a maximum radius of 100 km.
Regressions of observed distribution size change were carried out against either
Dx or Ripley’s L calculated for the radii (= “scales”) of 10, 20, 50 and 100 km,
combined with AOO calculated using 10 km cells.
In common with fractal dimension (Dij), Dx was positively related to AOO (R2
0.66-0.83, P < 0.001 for regressions of Dx at scales of 10, 20, 50 and 100 km against
AOO calculated at 10 km scale). Regressions of change against Dx and AOO included
significant positive effects of the former and significant negative effects of the latter,
with R2 ranging from 0.48 to 0.55 at the different spatial scales (phylogenetic GLS R2
ranged from 0.47 to 0.54) (Supplementary Table 5). Thus the relationship of distribution
change with Dx and AOO was very similar to its relationship with Dij and AOO.
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In contrast with Dij and Dx, Ripley’s L was strongly negatively related to AOO (R2
0.79-0.84, P < 0.001 for regressions of L at scales of 10, 20, 50 and 100 km against
AOO at 10 km scale), and was never significantly related on its own to distribution
change (P > 0.1). However, regressions of change against both L and AOO included
significant positive effects of both variables, with R2 ranging from 0.24 to 0.39 at the
different spatial scales (phylogenetic GLS R2 ranged from 0.23 to 0.39) (Supplementary
Table 6). Thus, including the measure of aggregation still substantially increased the
proportion of variation explained relative to that explained by area of occupancy alone
(NB. Regression of change against AOO, R2 = 0.16).
To test the consistency of the three measures used to quantify aggregation relative
to distribution size (Dij, Dx, L), we calculated the residuals of the linear regression of
each measure against AOO, and then carried out Spearman’s rank correlations among
these residuals. Residuals for Dij calculated at 10-100 km (the scale reported in the main
text) were significantly positively correlated with residuals for Dx and L at all spatial
scales (rs 0.49-0.85, P < 0.001). Residuals from Dx and L were significantly positively
correlated at all scales (Supplementary Table 7).
Other explanatory variables. Butterfly population densities were derived from
standardised counts of adult butterflies made at over 100 transect locations in the UK as
part of the British Butterfly Monitoring SchemeS13, S14. The density of each species on
occupied sections of transects (i.e. excluding transects or sections of transects that were
unsuitable or unoccupied) was calculated for 1980, 1990, and for the average of 19781982 transect counts, excluding species with visibility or identification problemsS3. No
measure of population density was significantly correlated with distribution change,
although density in 1978-82 was positively correlated with Dij (Spearman’s rank
correlation, n = 44 species, rs = 0.35, P = 0.02) and AOO (n = 44, rs = 0.33, P = 0.03).
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Butterfly species mobility was analysed using a published ranking of relative
mobility, based on a consensus of 24 butterfly ecologists in Britain and other European
countriesS3. Mobility was positively related to distribution change (Spearman’s rank
correlation, n = 51 species, rs = 0.39, P = 0.005), to Dij (rs = 0.59, P < 0.001) and to
AOO (rs = 0.48, P < 0.001), showing that mobile species tend to have increased, and to
have larger and more aggregated distributions than more sedentary species.
Nevertheless, in forward stepwise linear regressions using distribution change as
the dependent variable (either using species as independent data points or as
phylogenetically independent contrasts), the residual variation of change against Dij and
AOO was never significantly related to population density or relative mobility. It has
been shown for British butterflies that generalist, mobile species have increased more
than specialist and sedentary species, and that distribution change is positively related to
abundance change at monitored locationsS15. However, the effects of mobility and
population density appear to be related to the spatial patterns of aggregation that we
document, such that they do not add significant extra information on distribution
change.
Flanders butterflies. Flanders distribution sizes and fractal dimensions were based on
190,000 distribution records collected since 1830S16. Changes in distribution size were
calculated as in reference S17 using data from 150 Universal Transverse Mercator
(UTM) 5 km squares that were sampled intensively enough both before and after 1991
to record six widespread species in each 5 km square in both periods. For the remaining
species, proportional changes in distribution size in Flanders were the number of these
150 intensively sampled 5 km squares occupied pre-1991 subtracted from the number of
squares occupied during 1991-99, divided by the number of squares occupied pre-1991.
As for British butterflies, analysis included all resident butterfly species that have
regularly been observed in Flanders since 1970, apart from those species for which
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more than 40% of occupied grid squares in either time-period were migrants, vagrants
or deliberate introductionsS16. The analysis included 34 species, following the exclusion
of the six ubiquitous species used to identify the 150 distribution change sample squares
(that because of the sampling regime could neither decline nor increaseS17) and the five
species that became extinct in Flanders between 1970 and 1991 (supplementary
reference S16). Species included in analysis were as follows: Anthocharis cardamines,
Apatura iris, Aphantopus hyperantus, Araschnia levana, Aricia agestis, Boloria selene,
Callophrys rubi, Carterocephalus palaemon, Celastrina argiolus, Coenonympha
pamphilus, Coenonympha tullia, Gonepteryx rhamni, Hesperia comma, Heteropterus
morpheus, Hipparchia semele, Lasiommata megera, Limenitis camilla, Lycaena
phlaeas, Lycaena tityrus, Maculinea alcon, Maniola jurtina, Neozephyrus quercus,
Nymphalis polychloros, Ochlodes venata, Papilio machaon, Plebejus argus, Polygonia
c-album, Polyommatus icarus, Pyrgus malvae, Pyronia tithonus, Satyrium ilicis, Thecla
betulae, Thymelicus lineola, Thymelicus sylvestris.
Dij for each species in Flanders was calculated across a tenfold range of scales,
using log10 area of 5 km and 50 km UTM squares occupied in each time period. AOO at
10 km scale in Flanders was estimated by reading off the area of occupancy at the 10
km scale from each species’ 5-50 km scale-area curve. To deduce past changes in
Flanders we used the equation relating past change to 1995-99 distribution pattern and
size in British butterflies (change = 0.08 + 1.18 Dij – 0.39 AOO), combined with
Flanders scaling patterns (5-50 km) and area of occupancy (10 km) for 1991-99. To
predict future changes we used the equation for 1970-82 in British butterflies (change =
0.40 + 1.18 Dij – 0.44 AOO) combined with Flanders scaling patterns and area of
occupancy for pre-1991 distribution records. Phylogenetic GLS regressions for Flanders
butterflies used a phylogeny based on that presented for British butterflies in
supplementary reference S3. As with analyses for British butterflies, the phylogenetic
regressions suggested a weak relationship between phylogeny and distribution change
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(large values of α), and were consistent with those using species as independent
datapoints (Supplementary Table 8).
British plants. British plant distributions were mapped at the scale of 10 km over the
periods 1930-1969S18 and 1987-1999S19. The standardised residual of the positive linear
regression of the proportion of 10 km cells occupied by each species in Britain in the
later period versus the earlier period has been used as a measure of relative change in
distribution size, corrected for increasing recording effortS19. We analysed 292 rare and
scarce plant species, and found that the change index was significantly positively related
to Dij for 1987-1999 over 1-10 km (coeff: 0.032, P = 0.032) and marginally positively
related to Dij over 10-100 km (coeff: 0.025, P = 0.056) but unrelated to AOO calculated
at 1 km (coeff: 0.738, P = 0.757) (M. J. O. Pocock et al., unpublished data). Thus,
plants with more aggregated distributions have declined less than species with more
fragmented distributions, with a stronger relationship when aggregation is calculated at
a finer scale.
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